Differential and Integral Equations

Nonlinear infiltration with a singular diffusion coefficient

Gabriela Marinoschi

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This paper deals with the study of the nonlinear boundary-value problem with initial data, modelling incompressible water infiltration into a homogeneous, isotropic, unsaturated soil, for nonhomogeneous Dirichlet boundary conditions. For some well-known hydraulic models, Richards' equation that describes the evolution of the volumetric water content has the particularity that the diffusion coefficient blows up at a certain value of the soil moisture. In this paper, for a problem of this type, a result of existence and uniqueness of the solution is proved for the unsaturated flow, and its properties are deduced. Conditions under which saturation occurrence is possible are finally discussed.

Article information

Differential Integral Equations, Volume 16, Number 9 (2003), 1093-1110.

First available in Project Euclid: 21 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 76S05: Flows in porous media; filtration; seepage
Secondary: 35K57: Reaction-diffusion equations 47J35: Nonlinear evolution equations [See also 34G20, 35K90, 35L90, 35Qxx, 35R20, 37Kxx, 37Lxx, 47H20, 58D25] 47N20: Applications to differential and integral equations


Marinoschi, Gabriela. Nonlinear infiltration with a singular diffusion coefficient. Differential Integral Equations 16 (2003), no. 9, 1093--1110. https://projecteuclid.org/euclid.die/1356060559

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